How Many Years Does a Sum of Money Triple Itself at 10 Per Annum: Simple and Compound Interests

When considering the growth of a sum of money over time at a specific rate of interest, one often wonders how long it takes for the amount to triple. This article explores both simple and compound interests at a rate of 10 per annum to determine the tripling time.

Simple Interest Approach

The first method to determine the tripling time involves simple interest. Let's start with a principal amount of 100.

Simple Interest Calculation

Using the formula for simple interest:

A P (PRT / 100)

where:

A is the final amount, P is the principal amount, R is the rate of interest (10%), T is the time in years, PRT / 100 is the interest earned.

Setting A to 300 (to triple the principal), we get:

300 100 (100 × 10 × T / 100)

300 – 100 10T

10T 200

T 200 / 10 20 years

Therefore, in 20 years, a sum of money will triple itself at a simple interest rate of 10 per annum.

Understanding Compound Interest

For a more accurate representation of real-world financial growth, we can use the compound interest formula:

A P(1 r)^t

Where:

A is the final amount (3 times the principal), P is the principal amount, r is the annual interest rate (10% or 0.10), t is the time in years.

Compound Interest Calculation

Setting up the equation for tripling the amount:

3P P(1 0.10)^t

Dividing both sides by P:

3 1.10^t

To solve for t, take the logarithm of both sides:

log3 t × log1.10

solving for t:

t log(3) / log(1.10)

Calculating the logarithms using base 10:

log3 ≈ 0.4771

log1.10 ≈ 0.0414

t ≈ 0.4771 / 0.0414 ≈ 11.52 years

Thus, it takes approximately 11.5 years for a sum of money to triple itself at an interest rate of 10 per annum with compound interest.

Practical Example

Let's consider a practical example where the sum is P 100:

Money becoming triple means earning simple interest SI of 200.

Rate of interest R 10

Number of years required for the money to triple at the rate of 10 simple interest SI / (P × R) 200 / (100 × 10) 20000 / 1000 20 years.

Therefore, if, for example, the amount of money was 100, the simple interest would be 10 per annum. In 20 years, the simple interest would be 10 x 20 200, which is the original 100. The total amount would be 300, hence tripling in 20 years.

Conclusion

While both simple and compound interests are useful for understanding financial growth, the tripling time varies significantly. The simple interest approach suggests it takes 20 years, whereas the compound interest approach indicates a closer to 11.52 years.

Equipped with this knowledge, investors and financial analysts can make more informed decisions regarding investment timelines and growth projections.

Key Points

Simple Interest Formula: A P (PRT / 100) Compound Interest Formula: A P(1 r)^t Tripling Time: Simple Interest - 20 years, Compound Interest - 11.52 years